lmomgev {lmomco} | R Documentation

## L-moments of the Generalized Extreme Value Distribution

### Description

This function estimates the L-moments of the Generalized Extreme Value distribution given the parameters (xi, α, and kappa) from `pargev`. The L-moments in terms of the parameters are

λ_1 = xi + frac{α}{kappa}(1-Γ(1+kappa)) mbox{,}

λ_2 = frac{α}{kappa}(1-2^{-kappa})Γ(1+kappa) mbox{,}

tau_3 = frac{2(1-3^{-kappa})}{1-2^{-kappa}} - 3 mbox{, and}

tau_4 = frac{5(1-4^{-kappa})-10(1-3^{-kappa})+6(1-2^{-kappa})}{1-2^{-kappa}} mbox{.}

### Usage

    lmomgev(para)

### Arguments

`para` | The parameters of the distribution.

### Value

An R `list` is returned.

`L1` | Arithmetic mean.
`L2` | L-scale—analogous to standard deviation.
`LCV` | coefficient of L-variation—analogous to coefficient of variation.
`TAU3` | The third L-moment ratio or L-skew—analogous to skew.
`TAU4` | The fourth L-moment ratio or L-kurtosis—analogous to kurtosis.
`TAU5` | The fifth L-moment ratio.
`L3` | The third L-moment.
`L4` | The fourth L-moment.
`L5` | The fifth L-moment.
`source` | An attribute identifying the computational source of the L-moments: “lmomgev”.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`pargev`, `quagev`, `cdfgev`

### Examples

    lmr <- lmom.ub(c(123,34,4,654,37,78))
    lmr
    lmomgev(pargev(lmr))

[Package lmomco version 0.92 Index]